Using the given P-V diagram, the work done by an ideal gas along the path A B C D is :

Solution

Physics sir · 4 steps

Work is P Δ V on each straight piece. Watch the sign when the volume shrinks.

1. A to B. Pressure stays at P₀ while volume grows from 2V₀ to 3V₀. So W_(AB) = P₀(3V₀ - 2V₀) = +P₀V₀.
2. B to C. Volume stays at 3V₀, so the gas does not expand or contract. W_(BC) = 0.
3. C to D. Pressure stays at 2P₀ while volume falls from 3V₀ to V₀. The gas is compressed, so the work done by it is negative: W_(CD) = 2P₀(V₀ - 3V₀) = -4P₀V₀.

   W_(ABCD) = P₀V₀ + 0 - 4P₀V₀ = -3P₀V₀

4. So. The work done by the gas along ABCD is -3P₀V₀, which is option (b).

The idea to keep. On a P-V diagram, work by the gas is the area under the path: positive when moving right (expansion), negative when moving left (compression), zero on vertical lines.

Answer from the NTA final answer key. Solution by PrepWiser.